2-Loop Supersymmetric Renormalisation Group Equations Including R-Parity Violation and Aspects of Unification

We present the complete 2-loop renormalisation group equations of the superpotential parameters for the supersymmetric standard model including the full set of R-parity violating couplings. We use these equations to do a study of (a) gauge coupling unification, (b) bottom-tau unification, (c) the fixed-point structure of the top quark Yukawa coupling, and (d) two-loop bounds from perturbative unification. For large values of the R-parity violating coupling, the value of \alpha_S(M_Z) predicted from unification can be reduced by 5% with respect to the R-parity conserving case, bringing it to within 2\sigma of the observed value. Bottom-tau Yukawa unification becomes potentially valid for any value of \tan\beta\sim 2-50. The prediction of the top Yukawa coupling from the low \tan\beta, infra-red quasi fixed point can be lowered by up to 10%, raising \tan\beta up to a maximum of 5 and relaxing experimental constraints upon the quasi-fixed point scenario. For heavy scalar fermion masses of order 1 Tev the limits on the higher family \Delta L\not=0 operators from perturbative unification are competitive with the indirect laboratory bounds. We calculate the dependence of these bounds upon \tan \beta.